This document provides an overview of a lesson on converting units and using indices in A-Level Physics. The key learning objectives are to convert between units and their multiple and submultiples, and to correctly handle indices. Examples are given of converting between different units of length, area, volume, and density. Rules for multiplying, dividing, raising to powers, and taking roots are outlined for working with indices. Practice problems apply these rules for simplifying terms with indices and writing expressions as single powers.

1. A-level Physics
Unit G481:
Mechanics
Indices
More on units

2. Lesson focus
• Basic maths: converting units & indices
Learning objectives
At the end of the lesson you will be able to:
• convert between units and their multiple and submultiples;
• correctly handle indices.
Motion

3. Converting units LOs
Convert each of the following quantities:
a) 400 cm to m b) 24 x 104 mm into m c) 0.050 watt in mW
d) 2.5 x 10-3 kN to N e) n kW to W f) n milliwatt to W
g) 3.5 x 2.2 mA to A h) 3.4 x 103 x y gram to kg
Trickier
1. Convert an area of: a) 350 cm2 to m2 b) 0.06 m2 to cm2
2. Convert a volume of: b) 2.5 mm3 to m3 b) 0.07 m3 to mm3
3. Convert a density of 8 g per cm3 to kg per m3
Motion

4. Using indices - 1 LOs
1. Write as powers of ten:
a. 1/10 b) 1/10 000 c) 1/10-4
2. What is the reciprocal of:
a. 10-4 b) 102 c) 10-19
Motion

5. Using indices: rules LOs
General rules for using indices (‘powers’ or ‘exponents’) are:
multiplication 10a x 10b = 10a+b
division 10a/10b = 10a-b
raising to a power (10a)b = 10ab
meanings: y1/a = a√y (the ‘ath root of y’)
y a/b = b√ya (the ‘bth root of y to the a)
y0 = 1
Motion

6. Using indices - 2 LOs
1. Simplify the following:
a. y6 x y7 b. y8 ÷ y5 c. (y3)4 d. 3y2 x 4y3
2. Write as a single power:
a. 1/10 x 103 b. 1000 x 10-2 c. 104/10 d. 10-8 x 1012
e. 10-3 x 10-4 f. x-2 x x-2 g. x5 x x-2 h. 1/x2
i. 1/x-6 j. x8/x3 l. (x4)-6 m. √x3√(1/x5)
Motion